It turns out that this can be a rather polarizing question. My M8, SGS5, Nexus 5 and LG G3 have no specifics regarding charging.
Conversely my Note 3 puts up a nice message in the notification area once the battery is fully charged asking me to remove the charger.
I follow that and now many months after release day when I bought it, I'm enjoying exceptional battery life.
Because Samsung let out a batch of bad phones with faulty chargers resulting in fires, they started adding that nag message.
And then they insisted that the victims sign gag orders to not discuss it in order to get phones replaced.
None of that had to with design.
Nothing bad happens with the phone left on the charger.
Not dropping power below 40% is also nonsense.
It's not magic, it's about chemistry and physical structure.
Lower the charge level, rapidly deplete what's left and the heat will spike high and hard. If that happens, then the metal structures that make up part of the battery will deform. If that happens, lifetime goes down along with everything else.
Don't run your phone hot for prolonged periods at any charge level.
Don't force it to stay on when it tells you it's time to shut down.
Don't worry about leaving your phone on the charger, it will get disconnected and stay that way until the charge drops to around 96% and then connect to start charging again.
"Oh no, I left my phone on the charger and now it drops 5% in 5 minutes!"
No.
You take the phone off the charger and it takes 5 minutes or so to see the actual charge level.
Just like your laptop.
Same behavior, same reason, same technology.